Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0502
Another method of graphing parabolas is based on knowing where the vertex and axis of symmetry are located as a starting point. We can use the following information to find the vertex and the axis of symmetry for quadratic functions of the form
y = f(x) = ax2 + bx + c
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In this example we will graph f(x) = x2 – 2x – 3.
| 1. Find the axis of symmetry.
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| 2. Since the x=coordinate
of the vertex is on the axis of symmetry, substitute this value into
the function to find the y-coordinate.
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| 3. Choose any x-value near the axis of
symmetry to find another point on the parabola. We will choose x = 4.
Next, reflect this point across the axis of symmetry to locate a third point on the curve. In this example, that would be (–2, 5).
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| 4. Now we are ready to
finish the parabola by connecting our three points with a smooth
curve.
You should notice however, that we have found additional points to create the best picture possible for the function y = x2 – 2x – 3.
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